Question

Find the volume of tetrahedron whose coterminus edges are `7hat i+hatk; 2hati+5hatj-3hatk and 4 hat i+3hatj+hat k`

Answer 1

Volume of tetrahedron whose conterminus edges are `bara,barb and barc " is " 1/6[bara barb barc].`

`"Here " bara=7hati+hatk; barb=2hati+5hatj-3hatk;barc=4hati+3hatj+hatk.`

Volume of tetrahedron  `=1/6[bara,barb,barc]`

                                   `=1/6|[7,0,1],[2,5,-3],[4,3,1]|`

                                   `=1/6[7(5+9)-0(2+12)+1(6-20)]`

                                   `=1/6[98-0-14]`

                                   `=1/6[84]`

                                    = 14  

 Hence volume of tetrahedron is 14 cubic units.